To find the rate of change of the function from \( x = -2 \) to \( x = 2 \), we can use the formula for the rate of change:
\[ \text{Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
In this case:
- \( a = -2 \)
- \( b = 2 \)
From the table, we need to find the corresponding \( y \) values for these \( x \) values. However, it seems that the \( y \) value for \( x = -2 \) is not given. Let's analyze the given points:
- The provided points from the table:
- \( (0, 0) \)
- \( (2, -4) \)
- \( (4, -8) \)
To calculate the rate of change accurately, we'll also need the \( y \) value when \( x = -2 \). Since it's not provided in the table, we cannot directly calculate it.
Assuming \((−2, 4)\) is included to form a complete point:
From the given information, we have:
- \( f(-2) = 4 \)
- \( f(2) = -4 \)
Now we can calculate the rate of change:
\[ \text{Rate of Change} = \frac{-4 - 4}{2 - (-2)} = \frac{-8}{4} = -2 \]
Thus, the function's rate of change from \( x = -2 \) to \( x = 2 \) is \( -2 \).
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